There are `8.4xx10^(22)` free electrons per `cm^(3)` in copper. The current in the wire is `0.21A` (e=`1.6xx10^(-19)C`). Then the drifts velocity of electrns in a copper wire of `1mm^(2)` cross section, will be:-

Options

A. `2.12xx10^(-5)m/s`
B. `0.78xx10^(-5)m/s`
C. `1.56xx10^(-5)m/s`
D. None of these

Explanation

To solve the problem of finding the drift velocity of electrons in a copper wire, we will follow these steps:

### Step 1: Convert the number of free electrons from cm³ to m³
The number of free electrons given is \( n = 8.4 \times 10^{22} \) electrons/cm³. To convert this to m³, we use the conversion factor \( 1 \text{ cm}^3 = 10^{-6} \text{ m}^3 \).

\[ n = 8.4 \times 10^{22} \text{ electrons/cm}^3 \times 10^{6} \text{ cm}^3/\text{m}^3 = 8.4 \times 10^{28} \text{ electrons/m}^3 \]

### Step 2: Identify the given values
We have the following values:
- Current, \( I = 0.21 \, \text{A} \)
- Charge of an electron, \( e = 1.6 \times 10^{-19} \, \text{C} \)
- Cross-sectional area, \( A = 1 \, \text{mm}^2 = 1 \times 10^{-6} \, \text{m}^2 \)

### Step 3: Use the formula for drift velocity
The formula relating current, number density of charge carriers, charge, area, and drift velocity is given by:

\[ I = n \cdot e \cdot A \cdot V_d \]

From this, we can solve for the drift velocity \( V_d \):

\[ V_d = \frac{I}{n \cdot e \cdot A} \]

### Step 4: Substitute the values into the formula
Now we can substitute the values we have into the equation for drift velocity:

\[ V_d = \frac{0.21 \, \text{A}}{(8.4 \times 10^{28} \, \text{m}^{-3}) \cdot (1.6 \times 10^{-19} \, \text{C}) \cdot (1 \times 10^{-6} \, \text{m}^2)} \]

### Step 5: Calculate the drift velocity
Now, we can calculate \( V_d \):

1. Calculate the denominator:
\[ n \cdot e \cdot A = (8.4 \times 10^{28}) \cdot (1.6 \times 10^{-19}) \cdot (1 \times 10^{-6}) \]
\[ = 8.4 \times 1.6 \times 10^{28 - 19 - 6} = 13.44 \times 10^{3} = 1.344 \times 10^{4} \]

2. Now, substitute back into the drift velocity equation:
\[ V_d = \frac{0.21}{1.344 \times 10^{4}} \approx 1.56 \times 10^{-5} \, \text{m/s} \]

### Final Result
The drift velocity of electrons in the copper wire is approximately:

\[ V_d \approx 1.56 \times 10^{-5} \, \text{m/s} \]